## Inverse function and rotation matrix

To understand why graphs of inverse functions are symmetric about the $y = x$ line, try see this from a different point of view: symmetry about $y = x$ is equivalent to symmetry about the x-axis if you rotate the points by $-\pi / 4$, right?

Let’s verify it. Given one arbitrary point $p_1 = (x, y)$ in function (mapping) $f$, then $p_2 = (y, x)$ is in $f^{-1}$. Rotate both points by $-\pi/4$, we have:

Go ahead and see that $p_1'$ and $p_2'$ differ only in the sign of their x-coordinates!